##### longitudinal gdp data
cwar<-dget("http://www.stat.duke.edu/~pdh10/Teaching/567/Data/coldwar")
dim(cwar$GDP)
dimnames(cwar$GDP)

## untransformed data and decomposition
Y<- cwar$GDP - mean(cwar$GDP)
udv1<-svd(Y) 
par(mfrow=c(1,3))
hist(Y)       
plot(udv1$d,type="h",lwd=4,col="gray")
plotwtxt(udv1$u[,1:2],labels=rownames(Y))
abline(h=0,lty=2,col="gray")
abline(v=0,lty=2,col="gray")

## transformed data and decomposition
lY<-log(cwar$GDP) - mean( log(cwar$GDP) )
udv2<-svd(lY)
par(mfrow=c(1,3))
hist(lY)
plot(udv2$d,type="h",lwd=4,col="gray")
plotwtxt(udv2$u[,1:2],labels=rownames(lY))
abline(h=0,lty=2,col="gray")
abline(v=0,lty=2,col="gray")

isel<-c(8,14,55,59) 
rownames(Y)[isel] 

Ys<-Y[isel,]
matplot(t(Ys),type="l")
legend( 1,max(Ys), legend=rownames(Ys),lty=1:4,col=1:4,bty="n")

udv2$v[,2]  # represents growth (change) over time

## which is better? what should the criterion be?
udv1$d[1]^2/sum(udv1$d^2)
udv2$d[1]^2/sum(udv2$d^2) 

## a scale invariant measure
r<-1:2

M1<-  udv1$u[,r] %*% diag(udv1$d)[r,r] %*% t( udv1$v[,r] ) 
c1<-cor( rank(Y),rank(M1)) 

M2<-  udv2$u[,r] %*% diag(udv2$d)[r,r] %*% t( udv2$v[,r] )
c2<-cor( rank(lY),rank(M2))

c1
c2

(1-c1)/(1-c2)